DE102018117244B3 - Method for determining a rough path from a predetermined contour - Google Patents

Abstract

The invention relates to a method for determining a rough path from a predetermined contour for driving a processing machine, which has at least two mutually redundant drive devices for performing superimposed movements, wherein the contour is determined by a contour function, which sections at least by ascending indicated contour nodes P ₀ to P _{n + 1} and the contour intersections P ₀ to P _{n + 1} associated contour section functions p ₀ - p _n is defined and having a contour start node P _0, where the rough trajectory is determined by a rough trajectory function, which at least in sections by ascending indexed rough trajectory nodes Q ₀ to Q _{n + 1} and has a Grobbahnstartknotenpunkt Q ₀ , Grobbahnstartknotenpunkt Q _{0 is set} equal to the Konturstartknotenpunkt P ₀ and below
in a first iteration step from the contour nodes P _j to P _{n + 1} whose index value k is equal to or higher than the index value j of the respective output co-ordinate node Q _j , that contour node P _k with the smallest possible index value k is determined whose distance from the output co-ordinate node Q _j just fulfilled a predetermined distance condition, and
- in a second iteration step, a _j on the respective output rough trajectory node Q following respective sequence rough trajectory node Q _{j +} is determined _1, which lies on a connecting line between Q _j aand P _k, or between Q _j and a focus of the section contour P _j P _k.

Description

The present invention relates to a method for determining a rough path from a predetermined contour for driving a processing machine, which has at least two mutually redundant drive devices for carrying out superimposed movements.

STATE OF THE ART

Such processing machines are used for example in milling, laser cutting, water jet cutting or engraving of wood, metal or plastic workpieces or as drawing machines (plotters) to produce workpieces or character lines with a given two- or three-dimensional contour can. By means of the drive devices, a stationary or also a moving, in particular a rotating tool can be moved along the predetermined contour so that the workpiece has a desired final contour after completion of the machining.

Depending on the course of the desired final contour, the tool often has to travel longer distances within a short time and is therefore exposed to strong acceleration and / or deceleration forces. Processing machines, which have only a single drive device for each desired direction of movement of the tool, get here quickly to their performance limits. In order to meet the speed and / or acceleration limits of the drive device, often the machining speed must be reduced below an acceptable level.

To avoid this, so-called redundant drive devices are used for each direction of movement of the processing machine. For this purpose, on the one hand, a low-dynamic drive is provided, which can travel relatively long travels, but due to a higher mass, however, has only a small dynamic movement. In addition, a second, highly dynamic drive is provided, which can be moved on the one hand by means of the low-dynamic drive, and on the other hand is able to move the tool with high speed and high acceleration or deceleration, however, the maximum travel of the highly dynamic drive device in the rule is limited.

In order to be able to control such a processing machine with redundant drive devices for a respective movement direction, it is customary to divide the contour with which the workpiece is to be processed into a coarse track and a fine track. The low-dynamic drive is controlled with the data of the coarse track, while at the same time the highly dynamic drive with the data of the fine web is controlled.

Such a division of the contour into a rough path and a fine web and a corresponding control of the processing machine is basically known and is, for example, in DE 103 55 614 B4 and EP 0 594 699 B1 described. When calculating the coarse track, at least the limited travel path of the highly dynamic drive must be taken into account, since otherwise erroneous machining of the workpiece would take place. Advantageously, further limiting parameters are taken into account in the path calculation. As a rule, this has the consequence that the coarse track rather comprises low-frequency movement components, while the fine track has high-frequency movement components. In general, the calculation of the coarse track and the fine track proceeds in such a way that first a coarse track is determined and then the fine track is determined by subtracting the coarse track from the contour.

Another investigation procedure for a location-led grobbahn is in EP 1 963 935 B1 described. A computer is in this case given a position-led abzufahrende initial trajectory, the initial trajectory is described by an initial function, so that by inserting a scalar trajectory parameter in the initial function respectively a corresponding position on the initial trajectory is determined, the scalar trajectory parameter is different from the time and for a path traveled along the initial trajectory is characteristic. The computer subjects the initial trajectory as a function of the scalar trajectory parameter of a filter with low-pass characteristic and thus determines a coarse function, so that by inserting the scalar trajectory parameter into the coarse function a corresponding position on the coarse trajectory is determined. The low-pass characteristic is related here to the scalar path parameter. The computer determines the coarse function such that the distance of the coarse path from the initial trajectory is always below a predetermined barrier, regardless of the value of the scalar trajectory parameter.

In other words, in EP 1 963 935 B1 a method for calculating a coarse function, which would be run by a low-dynamic drive proposed, which is calculated by the fact that a dependent of a route parameter initial trajectory is low-pass filtered with respect to this route parameter. The low-pass filtered function is checked to see if a distance of this function to the initial trajectory is below a predetermined threshold over the entire range of the track parameter. If necessary, you can from the low-pass filtered function, further coarsening is made gradually to determine the coarse track as long as the aforementioned barrier is maintained.

In the dissertation "control of machine tools with redundant axes" of Messrs. Marco Bock from the Department of Mathematics and Computer Science, Physics, Geography of Justus Liebig University Giessen, submitted in August 2010 (http://geb.unigiessen.de/geb/ volltexte / 2011/7970 / pdf / BockMarco_2010_11_19.pdf) various other methods for determining a rough path from a given contour for the control of a processing machine are described.

According to a first exemplary embodiment, to determine the coarse function, first characteristic intermediate vectors with control points of a spline representation of the initial trajectory can first be determined. Based on this, second characteristic intermediate vectors can be determined from the first characteristic intermediate vectors of the spline representation which contain control points and which define a second intermediate path. The control points can be determined by a weighted or unweighted averaging of two immediately consecutive intermediate vectors of the first sequence. Based on this, third intermediate vectors can be calculated in a corresponding manner. After this two-time determination of the intermediate path, it now has to be determined whether a geometric distance of the intermediate path as coarse function from the initial path lies below the predetermined barrier along the path parameter. For this purpose, the spline vectors of the initial trajectory can be compared with the spline vectors of the intermediate trajectory of the coarse function in a simplified manner, wherein the maximum value of these distances results in an upper distance limit, which in turn can be compared with the barrier on compliance with the predetermined criterion.

In a second exemplary embodiment, based on a spline representation of the initial function for a multiplicity of scalar values of the path parameter, respective path positions on the initial trajectory can be determined. From these pairs of values, a first intermediate path is defined by the aforesaid scanning. A second intermediate trajectory of the coarse function within the interval of the scalar trajectory parameter may be determined by weighted or unweighted averaging of the positions on the first intermediate trajectory. The second intermediate web can be compared with respect to compliance with the barrier with the initial web or with the first scanned intermediate web, taking into account an auxiliary barrier.

Depending on the given contour, it may be the case that the known path separation methods can not provide satisfactory results. Under certain circumstances, the known methods can be very compute-intensive and require a correspondingly long computing time. It is also conceivable that the processing time resulting from the web decomposition does not correspond to the physical possibilities of the processing machine and is therefore prolonged.

It is therefore an object of the invention to provide a method of the type mentioned, which is improved over known methods.

DISCLOSURE OF THE INVENTION

The object is achieved by a method having the features of claim 1. Advantageous embodiments are specified in the dependent claims.

• - in einem ersten Iterationsschritt aus den Konturknotenpunkten P_j bis P_n+1 , deren Indexwert k gleich oder höher wie der Indexwert j des jeweiligen Ausgangsgrobbahnknotenpunkts Q_j ist, derjenige Konturknotenpunkt P_k mit kleinstmöglichem Indexwert k ermittelt wird, dessen Abstand von dem Ausgangsgrobbahnknotenpunkt Q_j gerade noch eine vorgegebene Abstandsbedingung erfüllt, und
• - in einem zweiten Iterationsschritt ein auf den jeweiligen Ausgangsgrobbahnknotenpunkt Qj folgender jeweiliger Folgegrobbahnknotenpunkt Q_j+1 ermittelt wird, der auf einer Verbindungslinie zwischen dem jeweiligen Ausgangsgrobbahnknotenpunkt Q_j und dem im ersten Iterationsschritt ermittelten Konturknotenpunkt P_k liegt, oder auf einer Verbindungslinie zwischen dem jeweiligen Ausgangsgrobbahnknotenpunkt Q_j und einem Schwerpunkt der Abschnittskontur zwischen P_j zu P_k liegt, und dessen Abstand von dem Ausgangsgrobbahnknotenpunkt Q_j dem mit einem Faktor gewichteten Abstand des im ersten Iterationsabschnitt ermittelten Konturknotenpunkts P_k von dem Ausgangsgrobbahnknotenpunkt Q_j entspricht, wobei sich der Faktor ergibt aus dem Quotienten aus der Bahnlänge s_j derjenigen Konturabschnittsfunktion p_j , deren Indexwert j gleich dem Indexwert j des jeweiligen Ausgangsgrobbahnknotenpunkts Q_j ist, und der Summe der Bahnlängen s_j bis s_k-1 der Konturabschnittsfunktionen p_j bis p_k-1 zwischen dem Konturknotenpunkt P_j , dessen Indexwert j gleich dem Indexwert j des jeweiligen Ausgangsgrobbahnknotenpunkts Q j ist und dem im ersten Iterationsschritt ermittelten Konturknotenpunkt P_k .

A method is proposed for determining a rough path from a predetermined contour for driving a processing machine, which has at least two mutually redundant drive devices for executing superimposed movements, wherein the contour is determined by a contour function, which sections at least by ascending indicated contour nodes P ₀ to P _{n + 1} and the contour nodes P ₀ to P _{n + 1} assigned contour section functions p ₀ to p _n is defined and a contour start node P ₀ wherein the coarse path is determined by a rough path function, which sections at least by Grobbahnknotenpunkte ascending indexed Q ₀ to Qn _{+ 1} is defined and a Grobbahnstartknotenpunkt Q ₀ initially having the Grobbahnstartknotenpunkt Q ₀ equal to the contour start node P ₀ is set and subsequently starting from a respective Ausgangsgrobbahnknotenpunkt _Qj and starting at the Grobbahnstartknotenpunkt Q ₀ an iteration is performed in which

• in a first iteration step from the contour nodes P _j to P _{n + 1} whose index value k is equal to or higher than the index value j of the respective output link node _Qj is that contour node P _k is determined with the smallest possible index value k whose distance from the output co-ordinate node Q _j just a predetermined distance condition met, and
• - In a second iteration step on the respective output co-ordinate node Qj the following respective sequence co-ordinate node _{Qj + 1} is determined on a connecting line between the respective Output coarse rail hub _Qj and the contour node determined in the first iteration step P _k is located, or on a connecting line between the respective Ausgangsgrobbahnknotenpunkt _Qj and a focus of section contour between P _j to P _k is located, and its distance from the Ausgangsgrobbahnknotenpunkt _Qj the factor-weighted distance of the contour node determined in the first iteration section P _k from the exit coaster junction _Qj corresponds, wherein the factor results from the quotient of the track length s _j that contour section function _pj , whose index value j is equal to the index value j of the respective output co-ordinate node _Qj is, and the sum of the track lengths s _j to s _k-1 the contour section functions _pj to p _k-1 between the contour node P _j whose index value j is equal to the index value j of the respective output co-ordinate node Q j and the contour node determined in the first iteration step P _k ,

The proposed method is very simple and delivers a final result for the coarse track already after a first pass. Multiple repetitions of the calculations are not required. A conversion or reparameterization of the contour or output path in a dependent of a scalar orbital shape form is also not required, which compared to known solutions can be saved already at the beginning of computer time.

The method is based on the surprisingly simple idea of constructing the coarse path iteratively, ie, node by node, starting from a starting point of the original contour. Starting from the starting node point of the contour or a rough path node point calculated in a preceding iteration _Qj becomes a succeeding co-ordinate node _{Qj + 1} determined. For this purpose, the Grobbahnstartknotenpunkt or the Ausgangsgrobbahnknotenpunkt _Qj set a window so that all points that lie within that window satisfy the stated predetermined distance condition. This distance condition is advantageously based on the maximum travel of the highly dynamic drive to ensure that by means of the fine web, which indeed represents the difference between the contour and the rough path, actually all target points can be approached according to the contour.

Starting from the Ausganggrobbahnknotenpunkt _Qj becomes that node P _k determines the contour that is just within this window, ie the next following node _{Pk + 1} The contour, ie the node with a higher index value by one, would already be outside this window. Conveniently, the first point below _{Pk + 1} which no longer satisfies the distance condition, and then the previous point becomes a point P _k selected.

If this contour node P _k is found, becomes an imaginary line from the exit coaster junction _Qj to the found contour node P _k pulled, with the newly to be determined following co-ordinate node _{Qj + 1} must be on this connecting line.

Alternatively, the imaginary line may also be from the exit coaster junction _Qj to a center of gravity of the section contour from the contour node P _j to the contour node P _k be pulled, with the newly to be determined following co-ordinate node _{Qj + 1} must be on this connecting line. The center of gravity can be, for example, by a geometric center of gravity of the contour section of the initial contour between a contour point P _j , which is the exit coaster junction _Qj is assigned, or this is geometrically closest, and just the distance criterion fulfilling contour point P _k be determined. In the simplest case, this can be the midpoint of the contour section between P _j to P _k but also a geometric center of gravity of all intermediate contour points P _j . P _{j + 1} ... to P _k on this contour section. A center of gravity formed in this way, or else according to another rule, is used to define that from the exit coaster junction _Qj outgoing imaginary line to which the following co-ordinate node point _{Qj + 1} is allocated.

In this respect, starting from the Ausganggrobbahnknotenpunkt _Qj the nearest output co-ordinate node _{Qj + 1} either follow an elongated contour, in which this in the direction of the farthest point P _k lies, or lie in the direction of a contour center of gravity, which is particularly suitable for strongly wavy or twisted contours.

The for unambiguous definition of the sequence co-ordinate node _{Qj + 1} required distance from the exit coaster junction _Qj is determined by the distance of the found contour node P _k from the exit coaster junction _Qj This distance is weighted by a factor which is determined by the quotient of the track length s _j the contour section function _pj whose index value j equals the index value j of the output co-ordinate node point underlying the respective search process _Qj corresponds, and the sum S of the track lengths s _j to s _k-1 the contour section functions _pj to p _k-1 between the contour node P _j , whose index value j is the index value j of the underlying exit link node _Qj corresponds, and the found contour node P _k ,

The follow-up co-ordinate point determined in this way _{Qj + 1} In a subsequent iteration, it becomes the new output co-ordinate node.

In contrast to the prior art, in the method according to the invention, no low-pass filtering is performed by a weighted or unweighted averaging of individual values. In addition, a check as to whether the distance of the coarse track from the contour is always below a predetermined barrier independent of a value of a scalar path parameter is not provided and also not required, since the selection of the follower path nodes ensures that the maximum travel path of the highly dynamic drive device is not exceeded.

It should be noted at this point that the aforementioned contour, which represents the basis of the web splitting according to the invention, does not necessarily have to represent the final contour of the workpiece to be machined. Optionally, here additionally a material removal can be taken into account, which is caused for example by the tool. For example, when using a milling cutter, the diameter of the milling head can be taken into account.

Advantageously, the contour function is a spline, in particular a spline of the first, third or fifth degree. Such descriptions are commonly used, for example, in CNC machining methods, where circles are usually described by a fifth degree spline.

According to an advantageous embodiment of the invention, the predetermined distance condition comprises at least a first and a second distance condition, wherein the contour node to be determined P _k has to fulfill at least one of the spacer conditions, wherein the first spacer condition comprises that for the contour node to be determined P _k the sum of the lengths of the tracks s _j - s _k between the contour node P _j whose index value j is equal to the index value j of the respective output link node _Qj is, and the contour node to be determined P _k is less than or equal to a predetermined limit Δ and the sum of the track lengths s _j - s _{k + 1} between the contour node P _j , whose index value j is equal to the index value j of the respective output co-ordinate node _Qj is, and that on the determined contour node P _k immediately following contour node _{Pk + 1} is greater than the predetermined limit Δ, and wherein the second spacing condition comprises that for the contour node to be determined P _k the distance between the contour node P _j , whose index value j is equal to the index value j of the respective output co-ordinate node _Qj is, and the respective output co-ordinate node _Qj is less than or equal to half of the predetermined limit Δ and the distance between the on the determined contour node P _k immediately following contour node P _{k + 1} and the respective Ausgangsgrobbahnknotenpunkt _Qj is greater than half of the predetermined limit Δ.

The predetermined limit value Δ, as already mentioned above, is expediently oriented on the travel path of the highly dynamic drive device. While the first pitch condition defines a bound for the path lengths of the original contour, the second pitch constraint vividly defines the size of the respective search window.

Regularly, only one of the two aforementioned conditions is selected uniformly for all iteration steps for a method run, wherein the condition can be selected in advance or initially chosen on the basis of characteristics of the contour. However, a combination of both conditions can be used for a procedure. Furthermore, it is conceivable to use the first condition and the second condition in sections, provided that the two spacer sub-conditions have different contour nodes P _k additional conditions may be established to decide which of the two points should be selected.

If, in the case of the first pitch sub-condition, no point satisfying the condition can be found, or if the found contour node has the same index value j as the output co-ordinate node _Qj , so becomes the contour node P _{j + 1} as the contour node to be determined P _k selected. The distance mentioned in the second spacing sub-condition need not necessarily be a distance in accordance with the Euclidean norm, but other norms, for example the maximum norm or the row sum norm, may also be used. When using the Euclidean norm, the above-mentioned search window has the form of a circle, while using the maximum norm the search window is rectangular, in particular square. Since usually the travel paths in the different directions of movement of the highly dynamic drive device are independent of each other, it is advisable to define the distance according to the maximum or line sum standard.

In accordance with a further advantageous embodiment, the rough path function is further provided by the respective coarse railway nodes Q ₀ - Qn _{+ 1} associated coarse track section functions q ₀ - q _n defined, wherein in the second iteration step the respective the exit coaster junction _Qj associated rough path section function _qj is formed by a linear function. Thus, the rough path section functions connect q ₀ - q _n the Grobbahnknotenpunkte Q ₀ - Qn _{+ 1} through respective straight lines.

According to an alternative embodiment, it is also possible that the rough path function further by respective the Grobbahnknotenpunkten Q ₀ to Qn _{+ 1} , associated rough track section functions q ₀ to q _n which is defined by means of a spline interpolation of Grobbahnknotenpunkte Q ₀ to Qn _{+ 1} has been generated. Advantageously, a third or higher degree spline is used here. While the above-mentioned linear functions can also be determined in the course of the iteration, it may make sense to perform the spline interpolation only after the determination of the coarse-path nodes for the determination of the coarse-path section functions.

list of figures

Further advantages emerge from the drawing and the associated description of the drawing. In the drawings, embodiments of the invention are shown. The drawing, the description and the claims contain numerous features in combination. The person skilled in the art will expediently also consider these features individually and combine them into meaningful further combinations.

• 1 eine schematische Darstellung einer Iteration eines erfindungsgemäßen Verfahrens zum Ermitteln einer Grobbahn, und
• 2 eine schematische Darstellung einer vorgegebenen Kontur und einer mittels des erfindungsgemäßen Verfahrens ermittelten zugehörigen Grobbahn.

It shows:

• 1 a schematic representation of an iteration of a method according to the invention for determining a coarse track, and
• 2 a schematic representation of a predetermined contour and a determined by means of the method according to the invention Grobbahn.

The method according to the invention is described below by way of example with reference to a path decomposition of a two-dimensional contour which is in a plane (FIG. X . Y ), of course a generalization to other dimensions is possible. The path separation takes place, for example, for a processing machine which has two redundant drive devices for each direction of movement. The contour can be described for example by splines first, third or fifth degree, as is customary for the operation of CNC processing machines. However, other descriptions of the contour may also be present.

A contour section j is through a starting point or contour node P _j = ( x _j . y _j ), a parameterization interval [0, s _j ] and a contour section function _pj defined, where s _j the arc length of the contour section is and the contour section function _pj describes the course of the contour section. In the examples according to 1 and 2 are the functions _pj linear functions.

Thus, the contour for which a coarse track is to be determined by a function ( P _j . s _j . _pj ), j = 0, ..., n.

It is noted that instead of a parameterization based on the path length s _j Any other parameterization can be selected, for example, a parameterization with time or in Cartesian coordinates x, y.

With the aid of the method according to the invention, a smoothed coarse track ( _Qj . s _j . _qj ), j = 0, ..., n are determined for driving the low-dynamic drive devices, so that the distance of this coarse track does not exceed a predetermined limit value Δ. The coarse way has to fulfill the following condition: $$\left|\left|p_j\left(s\right)-q_j\left(s\right)\right|\right|\le \mathrm{\Delta }.s\in \left[0s_j\right].j=0....n,$$

The process according to the invention is an iterative process. At the beginning, a Grobbahnstartknotenpunkt Q ₀ equal to the start node P ₀ set the contour. Within an iteration j, at least the following two steps are performed.

$${\left|\left|P_k\left(s\right)-Q_j\left(s\right)\right|\right|}_p\le \frac{\mathrm{\Delta }}{2},{\left|\left|P_{k+1}\left(s\right)-Q_j\left(s\right)\right|\right|}_p>\frac{\mathrm{\Delta }}{2}.$$

In a first step, a first contour node is created P _k with k ≥ j satisfying either the first or the second of the following two conditions: $${\displaystyle \underset{l=j}{\overset{k}{\Sigma }}{s}_l\le \mathrm{\Delta }.}{\displaystyle \underset{l=j}{\overset{k+1}{\Sigma }}{s}_l>\mathrm{\Delta }.}$$

$${\left|\left|P_k\left(s\right)-Q_j\left(s\right)\right|\right|}_p\le \frac{\mathrm{\Delta }}{2}.{\left|\left|P_{k+1}\left(s\right)-Q_j\left(s\right)\right|\right|}_p>\frac{\mathrm{\Delta }}{2},$$

Regularly, only one of the two conditions is for a process run 1 or 2 applied. The condition to be used may be fixed, or selected on the basis of performance characteristics such as continuity, curvature, etc. It is also conceivable that one of the two conditions is applied in sections.

If for the condition ( 1 ) no such point can be found or for the condition ( 2 ) k = j, then the contour node to be determined becomes P _k as the contour node P _{j + 1} Are defined.

Determining the contour node P _k with smallest possible index value k is for p = ∞, ie the maximum norm, in 1 illustrated. By calculating the distance according to the maximum standard, a search window F, within which the contour node to be determined must be located, has the shape of a square with the edge length Δ. As in 1 The point is clear P _k just inside the search window F, while the next point _{Pk + 1} already outside the search window. In this respect, the contour balance point P _k which just barely meets a distance norm while the next point _{Pk + 1} this already no longer met. Conveniently, the point is first _{Pk + 1} as the point that breaks the distance condition, and thus the previous point P _k identified.

die Summe S der Bahnlängen s_j bis s_k der Konturabschnittsfunktionen p_j bis p_k zwischen dem Konturknotenpunkt P_j , dessen Indexwert j gleich dem Indexwert j des jeweiligen Ausgangsgrobbahnknotenpunkts Q_j ist und dem im ersten Iterationsschritt ermittelten Konturknotenpunkt P_k berechnet. Die aufsummierten Bahnlängen s_j bis s_k sind in 1 mit Σs_I gekennzeichnet. Auf der Grundlage von S, s_j , Q_j und P_k wird ein Folgegrobbahnknotenpunkt $$Q_{j+1}=Q_j+\frac{s_j}{S}\left(P_k-Q_j\right)$$

sowie eine zugeordnete Grobbahnabschnittsfunktion $$q_j\left(s\right)=Q_j+\frac{s}{s_j}\left(Q_{j+1}-Q_j\right)$$

ermittelt.In a second iteration step, by means of the equation $$S={\displaystyle \underset{l=j}{\overset{k-1}{\Sigma }}{s}_l}.$$

the sum S of the track lengths s _j to s _k the contour section functions _pj to p _k between the contour node P _j whose index value j is equal to the index value j of the respective output link node _Qj and the contour node determined in the first iteration step P _k calculated. The accumulated track lengths s _j to s _k are in 1 marked with Σs _I. On the basis of S, s _j . _Qj and P _k becomes a sequence co-ordinate node $$Q_{j+1}=Q_j+\frac{s_j}{S}\left(P_k-Q_j\right)$$

and an associated rough path section function $$q_j\left(s\right)=Q_j+\frac{s}{s_j}\left(Q_{j+1}-Q_j\right)$$

determined.

The dashed line representing the exit coaster junction _Qj and the sequence co-ordinate node _{Qj + 1} connects, represents the rough path section function _qj ,

Subsequently, the next iteration j + 1 is carried out, the value of the following co-ordinate node determined in the iteration j _{Qj + 1} in the next iteration j + 1 forms the new output co-ordinate node.

In 2 is another contour ( P _j . s _j . _pj ), for which a coarse track ( _Qj . s _j . _Qj ) is also determined according to the method of the invention.

The determination of respective sequence co-ordinate nodes _{Qj + 1} starting from a Ausganggrobbahnknotenpunkt _Qj by finding a contour node just still within the search window F P _k and the associated coarse path section function q _j (s) takes place here in the same way as described with reference to FIG 1 has been described.

Claims (6)

Method for determining a coarse track from a predetermined contour for driving a machine tool, which has at least two mutually redundant drive devices for performing superimposed movements, wherein the contour is determined by a contour function, which sections at least by ascending indicated contour nodes (P ₀ - P _{n +1} ) and the contour nodes (P ₀ - P _{n + 1} ) associated contour section functions (p ₀ - p _n ) is defined and has a contour start node (P ₀ ), wherein the coarse track is determined by a Grobbahnfunktion which sections indexed at least by ascending Grobbahnknotenpunkte (Q ₀ - Q _{n + 1} ) is defined and has a Grobbahnstartknotenpunkt (Q ₀ ), wherein initially a Grobbahnstartknotenpunkt (Q ₀ ) is set equal to the Konturstartknotenpunkt (P ₀ ) and subsequently starting from a respective Ausgangsgrobbahnknotenpunkt (Q _j ) and starting at the Grobbahnstartknot enpunkt (Q ₀₎ is carried out one iteration, wherein - in a first iteration step from the contour nodes (P _j - P _n), the index value (k) is equal to or higher than the index value (j) of the respective output rough trajectory node (Q _j) is determining the contour node (P _k ) having the smallest possible index value (k) whose distance from the output coarse junction (Q _j ) still just satisfies a predetermined distance condition, and - in a second iteration step, a respective following coarse path node following the respective output co-ordinate node (Q _j ) (Q _{j + 1} ) located on a connecting line between the respective output co-ordinating node (Q _j ) and the contour node (P _k ) determined in the first iteration step, or on a connecting line between the respective output co-ordinating node (Q _j ) and a center of gravity of Section contour lies between (P _j ) to (P _k ), and its distance from the output sgrobbahnknotenpunkt (Q _j ) corresponding to the factor-weighted distance of the determined in the first iteration Absch nitt contour node (P _k ) of the Ausgangsgrobbahnknotenpunkt (Q _j ), wherein the factor is the quotient of the path length (s _j ) of those Contour portion function (p _j ) whose index value (j) is equal to the index value (j) of the respective output orbit node (Q _j ) and the sum (S) of the orbit lengths (s _j -s _k-1 ) of the contour portion functions (p _j -p _k-1 ) between the contour node (P _j ), whose index value (j) is equal to the index value (j) of the respective output coarse node (Q _j ), and the contour node (P _k ) determined in the first iteration step. Method according to Claim 1 , characterized in that the contour function is a spline, in particular a spline first, third or fifth degree. Method according to Claim 1 or 2 characterized in that the predetermined distance condition comprises at least a first and a second distance subcondition, wherein the contour node (P _k ) to be determined has to fulfill at least one of the distance subconditions, wherein the first distance subcondition comprises that for the contour node (P _k ) to be determined Sum of the path lengths (s _j -s _k ) between that contour node (P _j ) whose index value (j) is equal to the index value (j) of the respective output co-ordinate node (Q _j ) and the contour node (P _k ) to be determined smaller or equal a predetermined limit (Δ) and the sum of the track lengths (s _j -s _{k + 1} ) between the contour node (P _j ) whose index value (j) is equal to the index value (j) of the respective output orbit node (Q _j ), and the contour node (P _{k + 1} ) directly following the contour node (P _k ) to be determined is greater than the predetermined limit value (Δ), and wherein the two te spacer condition includes that is designed to be determined contour node (P _k) of the distance between the contour node (P _j), the index value (j) is equal to the index value (j) of the respective output rough trajectory node (Q _j), and the respective output rough trajectory node (Q _j ) is less than or equal to half of the predetermined limit value (Δ) and the distance between the contour node (P _{k + 1} ) directly following the contour node (P _k ) to be determined and the respective output co-ordinate node (Q _j ) is greater than half of predetermined limit value (Δ). Method according to one of the preceding claims, characterized in that the rough trajectory function further by respective the rough trajectory nodes (Q ₀ - _n Q _{+ 1)} associated with the coarse track section functions (q ₀ - q _n) is defined, and that the respective output rough trajectory node in the second iteration ( Q _j) associated with the coarse track section function (q _j) is formed by a linear function. Method according to one of Claims 1 to 4 Been produced, characterized in that the rough trajectory function further by respective the rough trajectory nodes (Q ₀ - Q _{n + 1)} associated with the coarse track section functions (q ₀ - - q _n) is defined, which by means of a spline interpolation of the rough trajectory nodes (Q _n Q ₀₎ is. Method according to one of Claims 3 to 5 , characterized in that the limit value (Δ) corresponds to a maximum travel of one of the drive devices.

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